jee_main_2025_28_jan_evening - Vector Algebra Topics

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QUESTION #52 Vector Operations and Components
Let A, B, C be three points in xy-plane, whose position vector are given by √(3) i+ j, i+√(3) j and a i+(1-a) j respectively with respect to the origin O. If the distance of the point C from the line bisecting the angle between the vectors OA and OB is 9√(2) then the sum of all the possible values of a is:
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QUESTION #53 Components of Vectors
If the components of a=α i+β j+γ k along and perpendicular to b=3 i+ j- k respectively, are (16)/(11)(3 i+ j- k) and (1)/(11)(-4 i-5 j-17 k), then α²+β²+γ² is equal to:
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JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%) | JEE Physics: Waves (+15.5%) | Electrostatics: Concentric Shells (-29.7%) | Modern Physics: Photoelectric Clones (+34.2%) | Mathematics: Definite Integrals (+18.1%) | Chemistry: Coordination Splitting (-11.4%)

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